Theoretical Physics 2 by Wolfgang Nolting

Author:Wolfgang Nolting
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

and as

Example: Linear Harmonic Oscillator

(see Example 2 in Sect. 2.2.2)

The configuration space is here the x-axis. The configuration path is built by all x for which | x | ≤ A.

By specification of the configuration path the mechanical problem is not yet solved because it remains unclear where the system finds itself at a certain point of time (Fig. 2.9).

Fig. 2.9Path of the linear harmonic oscillator in the configuration space

(2) Event Space

The path in the event space (q, t) is definitely calculable if 2S initial conditions are given. These can be the configurations at two different times, , or S generalized coordinates and the corresponding S generalized velocities at a certain point of time : Lagrange formalism event space.

Example: Linear Harmonic Oscillator

Because of S = 1 two initial conditions are necessary in order to fix uniquely the path in the event space (Fig. 2.10).

Fig. 2.10Path of the linear harmonic oscillator in the event space

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